Philosophy 290-4

The distinction between concepts and objects is crucial to Frege’s entire work. It determines the construction of his logic, his philosophy of mathematics, and his account of meaning and truth. The examination of how Frege wields these two notions can therefore serve as an entry into his work as a whole.

Frege has discussed the distinction between concepts and objects most famously in the essay “On Concept and Object” of 1892. That essay will therefore have to be at the center of our attention. But the distinction is already implicit in the construction of his logic in the Begriffsschrift (of 1879) where it serves to explain the distinction between first- and second level functions. It is absolutely crucial in The Foundations of Arithmetic (of 1884) where Frege argues that numbers are (abstract) objects rather than concepts. What he means here is further elaborated in the essay “Function and Concept” (1891) where Frege interprets concepts as a specific kind of function, e.g., truth-functions. This thesis is, in turn, connected with the claim that the values of truth-functions, the true and the false, are again abstract (logical) objects.

Frege’s assertions about the distinction between concepts and objects are often puzzling and sometimes downright paradoxical as in his claim that “the concept ‘horse’ is not a concept.” Many of these puzzles can be resolved and in doing so we come to see that Frege has made some genuine contributions to our understanding of the notions of concept and object. But we also discover real difficulties in his handling of those notions. While the thesis that value-ranges or, more narrowly speaking, classes are logical objects appears to follow directly from his conception, it is also the source of a logical contradiction from which Frege finds it difficult to extract himself. That contradiction threatens, in turn, his entire project of providing logical foundations for arithmetic.

Much of what Frege says about the distinction between concepts and objects remains, nevertheless, of philosophical interest. This is evident, for instance, from Donald Davidson’s recent book on truth and predication.